Regular Polygon Calculator

Use this calculator to find the perimeter and area of a regular polygon when you know the number of sides n and the side length s.

In the diagram, the side length is labeled s.

Step-by-step method

1. Identify what is given.
2. Write the formulas.
3. Substitute the values to calculate the perimeter.
4. Substitute the values into the area formula.
5. Calculate the area.

Formula:

Example 1: n = 6, s = 5

Step 1 - Identify what is given.

In this problem: The given values are n = 6 and s = 5.

Step 2 - Write the formulas.

In this problem: Use the formulas: P = n × s and A = (n × s²) / (4 × tan(π/n)).

Step 3 - Substitute the values to calculate the perimeter.

In this problem: Substitute into P = n × s: P = 6 × 5 = 30.

Step 4 - Substitute the values into the area formula.

In this problem: Substitute into the area formula: A = (6 × 5²) / (4 × tan(π/6)).

Step 5 - Calculate the area.

In this problem: Compute: n × s² = 6 × 25 = 150, 4 × tan(π/6) = 2.30940108. So A = 150 / 2.30940108 = 64.95190528.

Final answer: P = 30, A = 64.95190528

Example 2: n = 8, s = 3.5

Step 1 - Identify what is given.

In this problem: The given values are n = 8 and s = 3.5.

Step 2 - Write the formulas.

In this problem: Use the formulas: P = n × s and A = (n × s²) / (4 × tan(π/n)).

Step 3 - Substitute the values to calculate the perimeter.

In this problem: Substitute into P = n × s: P = 8 × 3.5 = 28.

Step 4 - Substitute the values into the area formula.

In this problem: Substitute into the area formula: A = (8 × 3.5²) / (4 × tan(π/8)).

Step 5 - Calculate the area.

In this problem: Compute: n × s² = 8 × 12.25 = 98, 4 × tan(π/8) = 1.65685425. So A = 98 / 1.65685425 = 59.14823228.

Final answer: P = 28, A = 59.14823228